Experimental and numerical study on the temporal and spatial nonlinearity evolution of focused wave

Extreme waves pose a significant threat to coastal structures. Focused wave, representing the average shape of extreme waves, is frequently employed to simulate extreme waves. Despite its convenience of generating large amplitude waves, the nonlinearity evolution of focused wave during propagation has been seldom explored. It is obvious that the nonlinearity would influence the wave shape and energy structure during focusing. This study investigates the temporal and spatial nonlinearity evolution experimentally and numerically. The experiment was conducted in a wave tank using a piston-type wavemaker. The numerical model was set up with geometry adopted from physical experiment in the commercial software FLUENT. The turbulence model RNG k–ε was employed, while the volume of fraction method was used to capture the air-water interface. The high-order harmonics were extracted from the recorded wave elevations by the four-phase decomposing method. The evolution of high-order harmonics and the energy structure were obtained. It is validated that the high-order harmonics can be reasonably estimated by multiplying linear harmonics by harmonic coefficients calculated by Stokes III or V wave theory. This paper enhances the understanding of temporal and spatial nonlinearity evolution of focused wave, which would be helpful for structure design and site selection. •The first four order harmonics are extracted based on four-phase decomposing method.•Nonlinearity increases with the energy transferring from linear harmonic to high order harmonics.•Quasi-quantitative features of energy structure and harmonic coefficients are obtained.•The profiles of focused wave group can be reconstructed satisfactorily with harmonic coefficients and linear harmonic.